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Teoriya Veroyatnostei i ee Primeneniya, 2008, Volume 53, Issue 3, Pages 458–471
DOI: https://doi.org/10.4213/tvp2442 (Mi tvp2442) 		 
This article is cited in 14 scientific papers (total in 14 papers)

On Distributions of First Passage Times and Optimal Stopping of AR(1) Sequences

A. A. Novikovab

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of Technology, Sydney
Full-text PDF (1185 kB) Citations (14)
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DOI: https://doi.org/10.4213/tvp2442
Abstract: Sufficient conditions for the exponential boundedness of first passage times of autoregressive (AR(1)) sequences are derived in this paper. An identity involving the mean of the first passage time is obtained. Further, this identity is used for finding a logarithmic asymptotic of the mean of the first passage time of Gaussian AR(1)-sequences from a strip. Accuracy of the asymptotic approximation is illustrated by Monte Carlo simulations. A corrected approximation is suggested to improve accuracy of the approximation. An explicit formula is derived for the generating function of the first passage time for the case of AR(1)-sequences generated by an innovation with the exponential distribution. The latter formula is used to study an optimal stopping problem.
Keywords: first passage time, autoregressive sequences, martingales, exponential boundedness, optimal stopping.
Received: 16.10.2007
Revised: 03.03.2008
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 3, Pages 419–429
DOI: https://doi.org/10.1137/S0040585X97983730
Bibliographic databases:
Language: Russian
Citation: A. A. Novikov, “On Distributions of First Passage Times and Optimal Stopping of AR(1) Sequences”, Teor. Veroyatnost. i Primenen., 53:3 (2008), 458–471; Theory Probab. Appl., 53:3 (2009), 419–429
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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